<html>
<head>
<title>Window</title>
</head>

<body>

<center>
<h1>POI V Stage 2 Problem 5</h1>
<h1>Window</h1>
</center>

<p>
We have a polygon chosen in the cartesian coordinate system.
Sides of the polygon are parallel to the axes
of coordinates. Every two consecutive sides are 
perpendicular and coordinates of every vertex
are integers. We have also given a window that is a rectangle
whose sides are parallel to the axes of coordinates.
The interior of the polygon (but not its periphery)
is coloured red. What is the number of separate red fragments
of the polygon that can be seen through the window?</p>

<h2>Example</h2>
Look at the figure below:

<center><img src="image/183.gif"></center>

There are two separate fragments of the polygon that can be seen 
through the window.

<h2>Task</h2>
Write a program that:
<ul>
<li> reads descriptions of a window and a polygon from the text file
OKN.IN;
<li>computes the number of separate red fragments of the polygon
that can be seen through the window;
<li>writes the result to the text file OKN.OUT.
</ul>

<h2>Input</h2>
In the first line of the input file OKN.IN there are four
integers x1, y1, x2, y2 from the range [0..10000], separated by
single spaces. The numbers x1, y1 are the coordinates of the
top-left corner of the window.
The numbers x2, y2 are the coordinates of the bottom-right corner of
the window.

The next line of the input file contains one integer n, 
4&lt;=n&lt;=5000, which equals the number of vertices of the polygon.

In the following n lines there are coordinates of polygon's vertices
given in anticlockwise direction, 
i.e the interior of the polygon is on the left side of its periphery
when we move along the sides of the polygon according to the
given order.
Each line contains two integers x, y separated by a single space,
0&lt;=x&lt;=10000, 0&lt;=y&lt;=10000.
The numbers in the (i+2)-nd line of the file OKN.IN, 1&lt;=i&lt;=n, 
are coordinates of the i-th vertex of the polygon. 

<h2>Output</h2>
In the first and only line of the output file OKN.OUT there
should be one integer - the number of separate red fragments
of the polygon that can be seen through the window.

<h2>Sample Input</h2>
<pre>
0 5 8 1
24
0 0
4 0
4 2
5 2
5 0
7 0
7 3
3 3
3 2
2 2
2 4
1 4
1 5
2 5
2 6
3 6
3 5
4 5
4 6
5 6
5 4
7 4
7 7
0 7
</pre>

<h2>Sample Output</h2>
<pre>
2
</pre>

</body>

</html>
